verification Taxonomic Roles with Linear Maps Large-Margin Loss with Dynamic Margins Guarantees to Ease Human Verification ge Semantics Jure Leskovec interest, Stanford University @{pinterest.com,cs.stanford.edu} %$// 1%$ 6+$4 4XHU\T H 1%$ H T 0 1%$ ,67<3(2) ,63/$<(52) ,6/($*8(2) ,03/,&,7('*(6(0$17,&6 [ V T1%$ 3 3 3 . [ Z 1%$ and (u, , ) is the desired margin dened as a function of the child, parent and non-parent nodes. We now derive the loss function to be minimized in order to satisfy the large-margin constraint (5). Denote by E(u, , 0) the degree to which a non-parent node 0 violates the large-margin constraint of child-parent pair (u, ): E(u, , 0) = max[0,s(u, 0) s(u, ) + (u, , 0)]. (6) When the large-margin constraint is satised, E(u, , 0) = 0 and the non-parent incurs no violation. Otherwise, E(u, , 0) > 0. The overall loss function L(T) is the total violation of the large- margin constraints by the non-parents corresponding to every child-parent pair (u, ): L(T) = ’ (u, )2E ’ 0 2V H(u) E(u, , 0) (7) The node embeddings w and linear-maps P1, . . . , Pk are jointly trained to minimize L(T) via gradient-descent. Given the trained parameters and a query node q < V having feature-vector eq, pre- dictions are made by ranking the taxonomy nodes in decreasing order of their taxonomic relatedness s(q, ). Using the fact that pairs and their cor L(T) Thus, minimizin on the sum of shor predictions and tr dicted parent node truth taxonomy. In ages non-parent n be scored relatively This guarantee experts; if A node, the taxonom around the predic nd the correct pa learned from the data [19]. We propose a principled dynamic margin func no tuning, learning or heuristics. We relate th shortest-path distances in the taxonomy between true parent nodes. Denote by d(·, ·) the undirec distance between two nodes in the taxonomy. W theorem, we bound the undirected shortest-path the highest-ranked predicted parent ˆ(u) = arg any true parent for every child node u: P 1. When (u, , 0) = d( , 0), L bound on the sum of the undirected shortest-path the highest-ranked predicted parents and true par ’ (u, )2E d( , ˆ(u)) L(T).